triangle family with integer sides and with rational bisector of angle A is given by with integers . Integer triangles with integer n-sectors of all angles There exist infinitely many non-similar triangles in which the three sides and the bisectors of each of the three angles are integers. There exist infinitely many non-similar triangles in which the three sides and the two trisectors of each of the three angles are integers. However, for n > 3 there exist no triangles in which the three sides and the (n – 1) n-sectors of each of the three angles are integers. Integer triangles with one angle with a given rational cosine Some integer triangles with one angle at vertex A having given rational cosine h / k (h < 0 or > 0; k > 0) are given by where p and q are any coprime positive integers such that p > qk. Integer triangles with a 60° angle (angles in arithmetic progression) All integer triangles with a 60° angle have their angles in an arithmetic progression. All such triangles are proportional to: with coprime integers m, n and 1 ≤ n ≤ m or 3m ≤ n. From here, all primitive solutions can be obtained by dividing a, b, and c by their greatest common divisor. Integer triangles with a 60° angle can also be generated by with coprime integers m, n with 0 < n < m (the angle of 60° is opposite to the side of length a). From here, all primitive solutions can be obtained by dividing a, b, and c by their greatest common divisor (e.g. an equilateral triangle solution is obtained by taking and , but this produces a = b = c = 3, which is not a primitive solution). See also Read, Emrys, "On integer-sided triangles containing angles of 120° or 60°", Mathematical Gazette 90, July 2006, 299−305. More precisely, If , then , otherwise . Two different pairs and generate the same triple. Unfortunately the two pairs can both be of gcd = 3, so we can't avoid duplicates by simply skipping that case. Instead, duplicates can be avoided by going only till . We still need to divide by 3 if gcd = 3. The only solution for under the above constraints is for . With this additional constraint all triples can be generated uniquely. An Eisenstein triple is a set of